Number of Theoretical Trays

The second method is a simplified one used to estimate the number of plates. This equation can only be used if both the equilibrium and operating 

Process flow sheet and stream summary using RateFmc block. 

Flo Bl values Status II LMts Final value Revious value Etna/ Tolerance 

is the liquid and gas molar flow rate, kmol/h m is the slope of equilibrium curve y 1/2 is the molar fraction of entering and exiting gas and 

%2 is the mole fraction of exiting and entering liquid Kremser method for theoretical trays (Stripper)  

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The relationship of this type of model to a tme differential analysis has been discussed for the case of linear equiHbrium and first-order kinetics (74,75). A minor extension of this work leads to the foUowing relations for a bed section in which dow rates of soHd and Hquid are constant. For the number of theoretical trays,... 

Point F on the figure represents conditions in the kettle or still with Xj, yj, or Xq, yo- Line DF represents slope of the operating line at minimum reflux. The step-wise development from point D cannot cross the intersection, F, where the slope intersects the equilibrium line, and leads to an infinite condition, as point F is approached. Thus, an infinite number of theoretical trays/stages is required, and... 

UK. = Light key component in volatile mixture L/V = Internal reflux ratio L/D = Actual external reflux ratio (L/D) ,in = Minimum external reflux ratio M = Molecular weight of compound Mg = Total mols steam required m = Number of sidestreams above feed, n N = Number of theoretical trays in distillation tower (not including reboiler) at operating finite reflux. For partial condenser system N includes condenser or number theoretical trays or transfer units for a packed tower (VOC calculations) Nb = Number of trays from tray, m, to bottom tray, but not including still or reboiler Nrain = Minimum number of theoretical trays in distillation tower (not including reboiler) at total or infinite reflux. For partial condenser system,... 

Nn = Number of theoretical trays above feed, or reference plate, n, but not including n Nm = Number of theoretical trays before feed tray Njra = Mols of immiscible liquid No = Mols of non-volatile material present or, number of theoretical trays/stages in column only, not reboiler or condenser Ng = Mols of steam... 

Sometimes the last term on right can be neglected. 7. Calculate number of theoretical trays, M. 

From values of Sj calculated (=Sg), read Ej, values from Figure 8-58 at the number of theoretical trays assumed in Step 2. Note that the Sg corresponds to the number of trays selected, hence will give a value for performance of the system under these particular conditions. 

Many designs are set up by assuming the number of theoretical trays, using best available information for tray efficiencies and then calculating the expected performance. A series of such studies might be made. 

The integrals in these equations are measures of the difficulty of the separation. Under some conditions they are roughly equal to the number of theoretical trays for the same change in concentration (yt, y2) or (xt, x2). Accordingly, they are called numbers of transfer units. 

The equilibrium curve also can be transformed into these coordinates. These transformations are useful for graphical determinations of numbers of theoretical trays rather than for determination of numbers of transfer units. Example 13.13 employs both sets of units. 

Numbers of Theoretical Trays and of Transfer Units with Two Values of kL/kG for a Distillation Process An equimolal mixture at its boiling point is to be separated into 95 and 5% contents of the lighter component in the top and bottoms products. The relative volatility is a- = 2, the minimum reflux is 1.714, and the operating reflux is 50% greater. The two values of kjJkQ to be examined are —1 and... 

Numbers of Theoretical Trays and of Transfer Units with Two Values of kJkG for a Distillation Process 402... 

The design of a tray tower for gas absorption and gas-stripping operations involves many of the same principles employed in distillation calculations, such as the determination of the number of theoretical trays needed to achieve a specified composition change (see Sec. 13). Distillation differs from absorption because it involves the separation of components based upon tne distribution of the various substances between a vapor phase and a liquid phase when all components are present in both phases. In distillation, the new phase is generated from the original phase by the vaporization or condensation of the volatile components, and the separation is achieved by introducing reflux to the top of the tower. 

Four theoretical trays have been stepped off for the key component (butane) on Fig. 14-11, and are seen to give a recovery of 75 percent of the butane. The operating lines for the other components have been drawn with the same slope and placed so as to give approximately the same number of theoretical trays. Figure 14-11 shows that equilibrium is easily achieved in fewer than four theoretical trays and that for the heavier components nearly complete recovery is obtained in four theoretical trays. The diagram also shows that absorption of the light components takes place in the upper part of the tower, and the final recovery of the heavier components takes place in the lower section of the tower. 

The left side of Eq. (14-55) represents the efficiency of absorption of any one component of the feed gas mixture. If the solvent is solute-free so that X2 = 0, the left side is equal to the fractional absorption of the component from the rich feed gas. When the number of theoretical trays N and the liquid and gas feed rates Lh and GjJ, have been fixed, the fractional absorption of each component may be computed directly, and the operating lines need not be placed by trial and error as in the graphical method described above. 

In addition to the critical design factors for finite-stage contactors of number of theoretical trays, maximum allowable vapor velocity, column efficiency, and pressure drop as discussed earlier, a number of other factors are of importance in the development of the design. These factors are discussed in the following sections. 

Estimate the number of theoretical trays needed to recover the dye intermediate. Enter Fig. 8.19 along its ordinate at a relative volatility of 2. For product purity of 99.5 percent, the graph shows that 11 stages are needed. 

Multicomponent distillation, 393 absorption factor method, 398 azeotropic, 420-426 bubblepoint (BP) method, 406-409 computer program references. 404 concentration profiles, 394 distribution of non-kevs. 395 Edmister method, 398,399 extractive, 412, 417-422 feed tray location, 397 free variables, number of 395 Lewis-Matheson method 404 MESH eauations. 405-407 molecular, 425-427 nomenclature, 405 number of theoretical trays, 397 packed towers, 433-439 petroleum, 411-415 reflux, minimum, 397 reflux, operating, 397 SC (simultaneous correction) method, 408-411... 

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